1. Field of the Invention
The present invention relates to an effective light source shape database generation method, an optical image calculation method, a recording medium, an exposure method, and a device fabrication method.
2. Description of the Related Art
A projection exposure apparatus which projects and transfers a circuit pattern formed on an original (reticle or mask) onto a substrate such as a wafer by a projection optical system is employed to manufacture a semiconductor device by using photolithography. The recent projection exposure apparatuses use resolution-enhanced techniques in order to cope with advances in the micropatterning of semiconductor devices (that is, to attain a high resolution).
Examples of the resolution-enhanced techniques are OAI (Off-Axis Illumination) techniques called modified illumination and oblique illumination, and OPC (Optical Proximity Correction) techniques. The OAI techniques obliquely irradiate the reticle with light by setting the illumination shape (illumination condition) to an annular shape or a multipole shape (for example, a dipole shape or a quadrupole shape). In addition, the OPC techniques correct the shape of an original pattern in accordance with a rule-based system or a model-based system using optical simulation by taking account of the influence of the shape of each pattern element and its peripheral elements on the shape precision in the design of the original pattern.
An original pattern is generally designed in accordance with the exposure conditions including, for example, the illumination shape and the numerical aperture (NA) of the projection optical system. Note that the diffraction direction and intensity of the light from the original change upon correcting the shape of the original pattern using the OPC techniques, so the illumination shape is often adjusted in order to form an optical image with a higher precision on the wafer (so as to form a desired illumination shape on the wafer). Under the circumstance, an original pattern is designed using, for example, a simulator which statistically derives the illumination shape by repeating the correction of the pattern shape (that is, the evaluation of the original pattern) by the OPC techniques and the adjustment of the illumination shape (see Japanese Patent No. 3342631 and Japanese Patent Laid-Open No. 2005-183981). Especially, Japanese Patent Laid-Open No. 2005-183981 discloses a technique for attaining optimization of the illumination shape by taking account of the OPC techniques, and therefore contributes to reducing a load on the design of an original pattern.
Such a simulator is called a lithography simulator and includes an optical calculation unit which performs arithmetic operation involved in optical factors and a non-optical calculation unit which performs arithmetic operations involved in non-optical factors (see Japanese Patent Laid-Open No. 2005-62750 and “Mathematical and CAD Framework for Proximity Correction” (1996, SPIE Vol. 2726, pp. 208-222, Optical Microlithography)). The optical calculation unit predicts an optical image to be formed on the wafer by an exposure optical system. The non-optical calculation unit includes a development calculation unit which predicts a process of developing a photosensitive agent (resist) applied on the wafer from the optical image calculated by the optical calculation unit, and a feature size calculation unit which predicts a change in the feature size of the pattern after the developed resist is etched.
To accurately predict the feature size of a pattern to be formed on the wafer, both the optical calculation unit and the non-optical calculation unit require calculation models with higher precisions. For example, the optical calculation unit adopts a vector calculation model. Also, various efforts are made to improve the model accuracy of each process modeled in the development calculation unit.
To improve the precision of a pattern formed on the wafer, it is demanded not only to precisely control the illumination shape and the design of an original by the OPC techniques but also to improve the calculation accuracy of the lithography simulator. To meet these demands, the optical calculation unit of the lithography simulator needs to obtain (calculate) a high-precision optical image. To achieve this object, an actual effective light source shape in the projection exposure apparatus is preferably used as an effective light source shape input to the lithography simulator.
However, the conventional lithography simulator receives an effective light source shape calculated from the design values and the arrangement of optical elements which constitute an illumination optical system. More specifically, this simulator calculates the effective light source shapes for respective conditions (for example, the selection and arrangement of optical elements) settable for (the optical elements which constitute) an illumination optical system, and compiles them into a database, thereby selecting and receiving one effective light source shape from the database in accordance with actually set conditions. Note that actual effective light source shapes in the projection exposure apparatus change depending on design factors (for example, manufacturing errors and arrangement errors) of the exposure optical system, so they differ from the effective light source shapes calculated from conditions settable for the illumination optical system.
It is plausible to measure actual effective light source shapes in the projection exposure apparatus for respective conditions settable for the illumination optical system, and compile them into a database. However, this is impractical because a large number of conditions are settable for the illumination optical system, so a considerable amount of time is taken to measure the effective light source shapes.
It is also plausible to measure only effective light source shapes corresponding to actually set conditions of conditions settable for the illumination optical system. However, conditions such as the illumination shape (that is, the conditions of the illumination optical system) are frequently changed in the design of an original pattern using, for example, the OPC techniques. This makes it necessary to measure the effective light source shape for every change of these conditions. In view of this, that solution is also impractical because it is impossible to dramatically decrease the number of times of measurement of the effective light source shape even when only effective light source shapes corresponding to conditions actually set for the illumination optical system are measured (that is, it takes much time to measure the effective light source shapes).